i thought the solution was interesting but I really dont understand the logic behind some of first moves. Is the solution really absolutely the best moves or are some of these puzzles more demonstrative/interesting than tactical?

The logic behind 1.Nc8 is that white cuts off the black rook from defending d8 threatening checkmate. The logic behind 1..., Nd5 is to prevent white from having a direct shot at d8 as 1..., Rxc8 loses to 2.Qd8+, Rxd8, 3.Rxd8#. The logic behind 2.Qb4+, is that black cannot play 2..., Nxb4 because of 3.Rd8#. The logic here is not readily visible, but the moves played are the best for black unless you consider massive material loss as better than losing to checkmate. Try looking through some of the earlier posts with diagrams to see how that is.